It would be FAR 91.119 - it appears there's a bit of a get-out for helicopters, but not on closer examination (at least to my way of seeing it):
"Except when necessary for takeoff or landing, no person may operate an aircraft below the following altitudes:
(c) Over other than congested areas. An altitude of 500 feet above the surface, except over open water or sparsely populated areas. In those cases, the aircraft may not be operated closer than 500 feet to any person, vessel, vehicle, or structure.
(d) Helicopters, powered parachutes, and weight-shift-control aircraft. If the operation is conducted without hazard to persons or property on the surface—
(1) A helicopter may be operated at less than the minimums prescribed in paragraph (b) or (c) of this section, provided each person operating the helicopter complies with any routes or altitudes specifically prescribed for helicopters by the FAA;…"
So if your helicopter is hazarding persons or property on the surface (and hitting a wire would probably count0, the 500' from the structure rule does apply...
But I stand to be corrected.